Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAX = 3e5 + 2;
int n;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= 1e5; i++) {
    long long x = i * (i + 1) >> 1;
    int l = 1, r = 1e5, mid;
    if (x > n) break;
    while (l <= r) {
      mid = (l + r) >> 1;
      long long y = mid * (mid + 1ll) >> 1;
      if (y + x > n)
        r = mid - 1;
      else if (y + x == n)
        return cout << "YES\n", 0;
      else
        l = mid + 1;
    }
  }
  cout << "NO";
  return 0;
}